Where one lives a little in Derby? (7)
I believe the answer is:
habitat
'where one lives' is the definition.
'a little in derby?' is the wordplay.
'a little' becomes 'abit' (synonyms).
'in' indicates putting letters inside.
'derby?' becomes 'hat' (derby is a kind of hat).
'abit' placed within 'hat' is 'HABITAT'.
(Other definitions for habitat that I've seen before include "Shop founded by Terence Conran" , "(Organism's) natural home" , "Environment in which groups normally live" , "Natural home of a plant or animal" , "Usual abode" .)